historically very interesting, heliocentric vs . geocentric universe
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Chapter 13: The Law of Gravity. Reading assignment: Chapter 13.1 to 13.5 Homework : OQ1, OQ2, OQ5, OQ8, 2, 3, 6, 10, 13, 14, 18, 28, 33 Due date: Tuesday April 12. Historically very interesting, heliocentric vs . geocentric universe - PowerPoint PPT PresentationTRANSCRIPT
• Historically very interesting, heliocentric vs. geocentric universe• The main cast: Copernicus, Brahe, Galileo, Kepler, Newton• Satellite motion
Chapter 13: The Law of GravityReading assignment: Chapter 13.1 to 13.5
Homework : OQ1, OQ2, OQ5, OQ8, 2, 3, 6, 10, 13, 14, 18, 28, 33
Due date: Tuesday April 12
Copernicus1473 – 1543
Brahe1546 – 1601
Galileo1564 – 1642
Kepler1571 – 1630
Newton1643 – 161727
- Ptolemy (100 –170 A.D.) geocentric model: Sun revolves around earth (Wrong!)
From astronomical observations: - Copernicus (1473-1543) heliocentric model: Earth & planets revolve around
sun- Brahe (1546 - 1601) Accurate observation of planetary motion - Galileo (1564 - 1642) (1610) supports the heliocentric model- Kepler (1571-1630), 1609: Laws I, II of planetary motion, - Kepler 1619: Law III of planetary motion
- Aristotle (384-322 B.C.) Heavier objects fall faster than light objects (Wrong!)- Galileo (1564 - 1642) Neglecting air resistance, all objects fall at same
acceleration
Geocentric vs. heliocentric model of earth
About falling objects
Newton’s Law of Universal GravitationEvery particle in the Universe attracts every other particle with a force of:
1 212 122
ˆm mF G rr
G… Gravitational constant G = 6.673·10-11 N·m2/kg2
m1, m2 …masses of particles 1 and 2
r… distance separating these particles
… unit vector in r direction12r̂
Experimentally confirmed.
Measuring the gravitational constant – Cavendish apparatus (1789)
What is the attractive force you (m1 = 100 kg) experience from the two people (m2 = m3 = 70 kg) sitting in front of you. Assume a distance r = 0.5 m and an angle q = 30° for both?
Black board example 13.1
q
Free-Fall Acceleration and the Gravitational Force
mgFRmMGF
g
E
Eg
2
Gravitational force:
Thus: 2E
E
Mg GR
g is not constant as we move up from the surface of the earth!
G is a universal constant (does not change at all).
a. What is the value of g in the ISS space station that is at an altitude of 400 km. Assume ME = 5.960·1024 kg and RE = 6.370·106 m.
b. Why does it feel like g = 0?
Black board example 13.2
Variation of g with altitude
The ISS photographed from shuttle Discovery in 2006.
From http://www.daviddarling.info/encyclopedia/I/ISS.html
Gravitational potential energy(similar equation for charge-charge interaction)
rmmGrU 21)(
• Notice the – sign • U = 0 at infinity
• U will get smaller (more negative) as r gets smaller. • “Falling down” means loosing gravit. potential energy.• Use only when far away from earth; otherwise use
approximation U = mgh.
(a) What is the escape speed of a particle on earth (ignore air resistance)?
A) ~10,000 m/s B) ~11,000 m/s C) ~20,000 m/s D) ~22,000 m/s
First Rocket Launch from Cape Canaveral (NASA); July 1950
Black board example 13.3
Kepler’s first two laws (1609):
I. Planets move in elliptical paths around the sun. The sun is in one of the focal points (foci) of the ellipse
II. The radius vector drawn from the sun to a planet sweeps out equal areas in equal time intervals (Law of equal areas).
Kepler’s laws about planetary motion
These laws hold true for any object in orbit
Area S-A-B equals area S-D-C
Kepler’s third law (1619):
III. The square of the orbital period, T, of any planet is proportional to the cube of the semimajor axis of the elliptical orbit, a.
Kepler’s laws about planetary motion
32 aT
Thus, for any two planets: 3
2
1
2
2
1
aa
TT
2 2
3
4 .S
T consta G M
G… Gravitational constant G = 6.673·10-11 N·m2/kg2
MS … central mass, (i.e. mass of sun for planet motion)
All nine eight planets of the solar system
Inner solar system:Mercury
Venus
Earth
Mars
Outer solar system:Jupiter
Saturn
Uranus
Neptune
(Pluto)